A281766 Number of 2 X n 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 4, 14, 40, 110, 280, 698, 1696, 4052, 9564, 22330, 51728, 118998, 272228, 619804, 1405456, 3175966, 7155320, 16078698, 36048008, 80656900, 180149700, 401740002, 894646944, 1989842814, 4420825196, 9811946668, 21757950712, 48209235558

Offset: 1

Author

R. H. Hardin, Jan 29 2017

Keywords

• nonn

Examples

			Some solutions for n=4:
..0..1..1..1. .0..0..0..0. .0..0..1..0. .0..1..0..0. .0..0..0..1
..0..0..0..0. .0..1..1..1. .0..1..0..1. .1..1..1..0. .0..0..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Row 2 of A281765.

Formula

Empirical: a(n) = 4*a(n-1) + a(n-2) - 16*a(n-3) - a(n-4) + 30*a(n-5) + 4*a(n-6) - 24*a(n-7) - 4*a(n-8) + 8*a(n-9).

Empirical g.f.: 2*x^2*(1 - x)*(1 + x)*(2 - x - 8*x^2 - x^3 + 6*x^4) / ((1 - 2*x)*(1 - x - 3*x^2 + 2*x^4)^2). - Colin Barker, Feb 20 2019